Binary Division Calculator
Divide one binary number by another and see the quotient and remainder in both binary and decimal. Enter the dividend and divisor as strings of 0s and 1s, and this calculator converts them to decimal, divides, then converts the results back to base-2.
Formula
dividend₂ ÷ divisor₂ → quotient (integer) and remainder, converted back to base-2
- Each binary number is converted to decimal, divided, and the integer quotient and remainder are converted back to binary.
- Binary division works exactly like long division in base-10, but every digit is either 0 or 1.
- Inputs must contain only the digits 0 and 1. A leading '0b' prefix is accepted and ignored.
- The quotient is the whole number of times the divisor fits into the dividend; the remainder is what is left over.
- Dividing by zero is undefined, so a divisor of 0 returns an error message.
1100 ÷ 10
Inputs
- Dividend (binary): 1100
- Divisor (binary): 10
1100₂ = 12 and 10₂ = 2. 12 ÷ 2 = 6 with remainder 0, so the quotient is 110₂ (6) and the remainder is 0.
Frequently asked questions
How does binary division work?
It follows the same long-division process as decimal, comparing the divisor against the leading bits of the dividend, but each quotient digit can only be 0 or 1.
What is the remainder?
The remainder is the amount left over when the divisor no longer fits into the dividend a whole number of times — the same idea as remainders in decimal division.
What if the numbers do not divide evenly?
This calculator returns the integer quotient plus a remainder. For example, 1011₂ (11) ÷ 10₂ (2) gives a quotient of 101₂ (5) and a remainder of 1.
Why does dividing by zero fail?
Division by zero is mathematically undefined in any base, so entering a divisor of 0 (or empty) returns an error instead of a result.
Can I enter a '0b' prefix?
Yes. A leading 0b (the common notation for binary literals) is stripped automatically, so both 0b1100 and 1100 are treated the same.